Could Fermat’s theorem and the principle of least action apply to the atmosphere’s response to increasing CO2? And show that a vast energy expenditure to heat atmosphere and ocean, is contrary to these laws? In other words, call into question whether increasing the trace gas CO2 really does heat the ocean and atmosphere.
The principle of least action states that the universe will choose the path between two states that minimises the action. This principle is a generalisation of Fermat’s theorem which requires light to take the path between two locations that minimises the travel time.
The principle of least action can be extended to any system evolving between two states. It is the founding assumption behind Noether’ theorem that is required to explain why Einsteinian relativity does not break conservation of energy.
Amalie Emmy Noether (she preferred the name Emmy) was a German mathematician who was born in 1882 – 13 years after my grandfather. In that time she was (sadly and inevitably) under-recognised as a female academic, but made important contributions to abstract algebra and theoretical physics that later would grow further in importance in cosmology and quantum physics.
Noether’s theorem is fundamental. It allows calculation of the true conserved quantities for any system that is evolving according to the principle of least action. (As long as we can identify the system’s symmetries.) Noether’s theorem is used in both cosmology and quantum physics.
Maybe the principle of least action could apply to atmospheric thermodynamics. For instance, the CO2 concentration in air increases. How will the atmosphere’s state evolve as a result? Conventionally we are told that the atmosphere’s response to a small increase in this trace gas is to summon up vast quantities of energy to increase the temperature of both atmosphere and ocean. This is an enormous thermodynamic response to this tiny trace gas perturbation, that transgresses the principle of least action.
However, a response by the system rearranging its structure, changing for instance water vapour content or the emission height, or adjustment of convection or even radiative interactions, could lead the system toward a new equilibrium with much less expenditure of energy. And thus fulfil the laws of least action, Noether’s and Fermat’s theorems. Miskolczi’s hypothesis was of this nature – a rearrangement of the emission structure without temperature change.
On the other hand, response to the tiny adjustment of CO2 amount by heating up the whole atmosphere and ocean, is the exact opposite of what one would expect in fulfilment of the principle of least action. It’s the principle of most action, and most (empty) heat and noise.